Hasan al-Titi, Al Jazeera's correspondent in Nablus, said around 100 military vehicles stormed the city on Thursday morning.
The operation was directed at the east of the old town and the areas of Ras al-Ain and Krum Aashur, he said.
Later in the day, Al Jazeera's correspondent Shireen Abu Aqla said troops withdrew from Nablus after the operation.
The Israeli army said soldiers had spotted an armed man during an operation and had shot him.
A spokesman said the man did not fire at its forces.
Medical staff said he died of his wounds before he could be taken to a hospital.
The Israeli forces used tear-gas bombs and rubber bullets, which resulted in some seven Palestinians sustaining injuries, one of them seriously, Abu Aqla said.
The operation began as children were making their way towards school and several students were reported to have fainted due to tear-gas bombs thrown by Israeli forces.
The troops subequently surrounded a number of buildings in the old town after midnight.
Abu Aqla said the Israeli forces continued their search and destroy operations until Thursday morning.
However, the "wanted" Fatah activists were able to escape, she quoted Palestinian sources as saying.
Other witnesses said an Israeli force succeed in arresting three Palestinians from one house, but they were not among the "wanted" men.
The operation resulted in many buildings in Nablus's historic old town suffering damage, Abu Aqla said.